#define DB false

#include "randomc.hpp"
#include <algorithm>

#include "probdist.hpp"
//#include "tex.h"
#include "mat.hpp"
#include "cnvt.hpp"

using namespace std;

StochasticLib ProbDist::STO( 7601014 );

const double ProbDist::ap[] = { .7, .75, .8, .85, .9, .95, .98 };
const unsigned ProbDist::apSize = 7;
const unsigned ProbDist::ll = ( unsigned )1e3;

const double ProbDist::plottingSmoothingFactor = 0.1;
const double ProbDist::PLOTTING_HALF_WIDTH_IN_STD = 3.0;

double ProbDist::getNormInv( double p ) {
   assert( p > norminv_precision && p < 1-norminv_precision );
   unsigned n;
   double m,v,q;

   q = ( p<.5 )?.5-p:p;

   m = ( q-.5 )/norminv_precision;
   n = ( unsigned )m;

   v = norminv[n]*( ( double )( n+1 )-m )+norminv[n+1]*( m-( double )n );

   if( p < .5 ) return -v;
   else return v;
}

double ProbDist::getNormPDF( double xx ) {
   if( xx < normx[0] || xx > normx[numBins-1] ) return 0.0;

   size_t s1 = ( size_t )( unsigned )( ( xx-normx[0] )/xinc );
   size_t s2 = s1 + 1;

   return cnvt::interpolate( xx, normx[s1], normpdf[s1], normx[s2], normpdf[s2] );
}

double ProbDist::getNormCDF( double xx ) {
   if( xx < normx[0] ) return 0.0;
   if( xx > normx[numBins-1] ) return 1.0;

   size_t s1 = ( size_t )( unsigned )( ( xx-normx[0] )/xinc );
   size_t s2 = s1 + 1;

   return cnvt::interpolate( xx, normx[s1], normcdf[s1], normx[s2], normcdf[s2] );
}

double * ProbDist::linSpace( double s, double e, unsigned num ) {
   assert( e > s );

   double inc = ( e-s )/( double )num;

   double * x = new double[num];

   for( size_t i = 0; i < num; i ++ )
      x[i] = s + inc * ( double )i;

   return x;
}

ProbDist::ProbDist( double * sm, unsigned n )
   : byDist( false ), hasEvaluated( false ), hasXPCAssigned( false ), sim( sm ), N( n ) {
   init();

   mean = 0.0;
   std = 0.0;
   for( unsigned i = 0; i < N; i ++ ) {
      mean += sim[i];
      std += sim[i]*sim[i];
   }

   mean /= ( double )N;
   std = sqrt( std/( double )N - mean*mean );
}

ProbDist::ProbDist( const string & detVal )
   : byDist( true ), type( "fixed" ), hasEvaluated( false ), hasXPCAssigned( false ), N( 0 ) {
   mean = atof( detVal.c_str() );
   std  = 0.0;

   init();
}

ProbDist::ProbDist( double detVal )
   : byDist( true ), type( "fixed" ), hasEvaluated( false ), hasXPCAssigned( false ), N( 0 ) {
   mean = detVal;
   std  = 0.0;

   init();
}

ProbDist::ProbDist( const string & dist, unsigned n, double mn, double sd )
   : byDist( true ), type( dist ), N( n ), hasEvaluated( false ), hasXPCAssigned( false ) {
   if( type == "uniform" ) {
      mean = mn-sqrt( 3.0 )*sd;
      std  = mn+sqrt( 3.0 )*sd;
   }
   else {
      mean = mn;
      std  = sd;
   }

   montecarlo();

   init();
}

ProbDist::ProbDist( const ProbDist & pd, double mn, double sd )
   : byDist( pd.byDist ), type( pd.type ), N( pd.N ),
     hasEvaluated( pd.hasEvaluated ), hasXPCAssigned( pd.hasXPCAssigned ) {
   if( hasEvaluated ) {
      mean = pd.mean * sd + mn;
      std = pd.std * sd;

      pctl = new double[apSize];
      for( unsigned i = 0; i < apSize; i ++ )
         pctl[i] = pd.pctl[i] * sd + mn;
   }

   if( hasXPCAssigned ) {
      x = new double[numBins];
      pdf = new double[numBins];
      cdf = new double[numBins];

      for( unsigned i = 0; i < numBins; i ++ ) {
         x[i] = pd.x[i] * sd + mn;
         pdf[i] = pd.pdf[i] / sd;
         cdf[i] = pd.cdf[i];
      }
   }

   if( N != 0 ) {
      sim = new double[N];
      for( unsigned i = 0; i < N; i ++ ) sim[i] = pd.sim[i] * sd + mn;
   }

   return;
}

double ProbDist::getPercentilePoint( double a ) {
   evalMSP();

   for( unsigned i = 0; i < apSize; i ++ )
      if( ap[i] == a ) return pctl[i];

   assert( false );
   return 0.0;
}

double * ProbDist::getAddedSimCopy( double a ) const {
   double * ns = new double[getNumberOfSimPoints()];

   for( unsigned i = 0; i < getNumberOfSimPoints(); i ++ ) ns[i] = sim[i] + a;

   return ns;
}

double ProbDist::getCDF( double xx ) {
   assignXPC();

   if( xx < getXMin() ) return 0.0;
   if( xx > getXMax() ) return 1.0;

   const double inc = ( x[1]-x[0] );

   size_t idx1 = ( size_t )( unsigned )( ( xx-getXMin() )/inc );
   size_t idx2 = idx1 + 1;

   return cnvt::interpolate( xx, x[idx1], cdf[idx1], x[idx2], cdf[idx2] );
}

double ProbDist::getPDF( double xx ) {
   assignXPC();

   if( xx < getXMin() ) return 0.0;
   if( xx > getXMax() ) return 0.0;

   const double inc = ( x[1]-x[0] );

   size_t idx1 = ( size_t )( unsigned )( ( xx-getXMin() )/inc );
   size_t idx2 = idx1 + 1;

   return cnvt::interpolate( xx, x[idx1], pdf[idx1], x[idx2], pdf[idx2] );
}

ProbDist & ProbDist::operator+ ( const ProbDist & pd ) const {
   // if both are gaussian, it's easy to add
   if( isByDist() && pd.isByDist() && getDistType() == "normal" && pd.getDistType() == "normal" )

      return *( new ProbDist( "normal",getNumberOfSimPoints(), getMean()+pd.getMean(), sqrt( getSTD()*getSTD()+pd.getSTD()*pd.getSTD() ) ) );

   assert( getNumberOfSimPoints() == 0 || pd.getNumberOfSimPoints() == 0 || getNumberOfSimPoints() == pd.getNumberOfSimPoints() );

   if( getNumberOfSimPoints() == 0 && pd.getNumberOfSimPoints() == 0 ) {
      return *( new ProbDist( getMean() + pd.getMean() ) );
   }
   else if( getNumberOfSimPoints() == 0 ) {
      if( pd.isByDist() )
         return *( new ProbDist( pd.getDistType(), pd.getNumberOfSimPoints(),
                                 pd.getMean()+getMean(), pd.getSTD() ) );
      else
         return *( new ProbDist( pd.getAddedSimCopy( getMean() ),
                                 pd.getNumberOfSimPoints() ) );
   }
   else if( pd.getNumberOfSimPoints() == 0 ) {
      return ( pd + ( *this ) );
   }
   else if( getNumberOfSimPoints() == pd.getNumberOfSimPoints() ) {
      double * sm = new double[getNumberOfSimPoints()];

      for( unsigned i = 0; i < getNumberOfSimPoints(); i ++ )
         sm[i] = getSimPoint( i ) + pd.getSimPoint( i );
      return *( new ProbDist( sm,getNumberOfSimPoints() ) );
   }
   else {
      assert( false );
   }
}

ostream & ProbDist::xMatVecToOstream( ostream & os ) {
   assignXPC();

   for( size_t k = 0; k < numBins; k ++ )
      os << x[k] << ';' << endl;

   return os;
}

ostream & ProbDist::pdfMatVecToOstream( ostream & os ) {
   assignXPC();

   for( size_t k = 0; k < numBins; k ++ )
      os << pdf[k] << ';' << endl;

   return os;
}

ostream & ProbDist::cdfMatVecToOstream( ostream & os ) {
   assignXPC();

   for( size_t k = 0; k < numBins; k ++ )
      os << cdf[k] << ';' << endl;

   return os;
}

ostream & ProbDist::cdfMatlabToOstream( ostream & os ) {
   assignXPC();

   size_t n = numBins;

   os << "X = [ ..." << endl;
   for( size_t k = 0; k < n; k ++ ) os << x[k] << ';' << endl;
   os << "];" << endl;
   os << endl;

   os << "Y = [ ..." << endl;
   for( size_t k = 0; k < n; k ++ ) os << cdf[k] << ';' << endl;
   os << "];" << endl;
   os << endl;

   double p9 = getPercentilePoint( .9 );
   os << "figure;" << endl;
   os << "plot(X,Y);" << endl;
   os << "hold on;" << endl;
   os << "ax = axis;" << endl;
   os << "line( [ax(1) " << p9 << " " << p9 << " ], "
      << ".9*[1 1 0], ..." << endl;
   os << "      'Color', 'r', 'LineStyle', '-.' );" << endl;
   os << "xlabel( 'mean=" << getMean() << ", std=" << getSTD()
      << ", 90per=" << p9 << "' );" << endl;
   os << "hold off;" << endl;
   os << endl;

   return os;
}

void ProbDist::montecarlo() {
   assert( isByDist() );

   sim = new double[N];

   if( type == "normal" ) {
      
      for( size_t i = 0 ; i < N; i ++ ) {
         sim[i] = STO.Normal( mean, std );
      }
   }
   else if ( type == "uniform" ) {
      
      for( size_t i = 0 ; i < N; i ++ ) {
         sim[i] = mean+( std-mean )*drand48();
      }
   }
   else {
      assert( false );
   }
}

void ProbDist::init() {
   if( !byDist ) return;

   pctl = new double[apSize];

   if( type == "normal" ) {
      
      for( unsigned i = 0; i < apSize; i ++ ) {
         pctl[i] = mean + std * getNormInv( ap[i] );
      }
   }
   else if( type == "uniform" ) {

      for( unsigned i = 0; i < apSize; i ++ ) {
         pctl[i] = mean + ( std-mean )*ap[i];
      }
   }
   else if( type == "fixed" ) {
      for( unsigned i = 0; i < apSize; i ++ ) {
         pctl[i] = mean;
      }
   }
   else {
      assert( false );
   }

   hasEvaluated = true;
}

void ProbDist::evalMSP() {
   if( hasEvaluated ) return;

   assert( !isByDist() );

   // calculate quantiles
   double * sortedSim = new double[N];

   // assign to sortedSim
   for( unsigned i = 0; i < N; i ++ ) {
      sortedSim[i] = sim[i];
   }

   // sort
   sort( sortedSim, sortedSim+N );

   pctl = new double[apSize];

   for( unsigned i = 0; i < apSize; i ++ ) {
      pctl[i] = sortedSim[( unsigned )( ap[i]*( double )N )];
   }

   delete sortedSim;

   hasEvaluated = true;

   return;
}

void ProbDist::assignXPC() {
   
   if( hasXPCAssigned ) { return; }

   pdf = new double [numBins];
   cdf = new double [numBins];

   if( byDist ) {
      x = new double [numBins];

      if( type == "normal" ) {
         double istd = 1.0/std;

         for( unsigned k = 0; k < numBins; k ++ ) {
            x[k] = mean+std*normx[k];
            pdf[k] = normpdf[k]*istd;
            cdf[k] = normcdf[k];
         }
      }
      else if( type == "uniform" ) {
         double inc = 2.0*( std-mean )/( double )numBins;
         double val = 1.0/( std-mean );

         x[0] = 1.5*std-.5*mean;
         pdf[0] = cdf[0] = 0.0;

         for( unsigned k = 1; k < numBins; k ++ ) {
            x[k] = x[k-1] + inc;
            pdf[k] = ( x[k] > mean && x[k] <= std )? val:0.0;
            if( x[k] <= mean ) cdf[k] = 0.0;
            else if( x[k] <= std ) cdf[k] = ( x[k]-mean )*val;
            else cdf[k] = 1.0;
         }
      }
      else {
         cerr << type << endl;
         assert( false );
      }
   }
   else {
      // calculate pdf and cdf with smoothing

      double _mean = getMean();
      double _std = getSTD();

      x = ProbDist::linSpace
          ( _mean - PLOTTING_HALF_WIDTH_IN_STD * _std,
            _mean + PLOTTING_HALF_WIDTH_IN_STD * _std, numBins );

      ProbDist::getPDFCDF( pdf, cdf, x, numBins, sim, N, _std );

   }

   hasXPCAssigned = true;

   return;
}

void ProbDist::doubleVectorToSmoothedPDF( vector<double> & x, vector<double> & y, const vector<double> & samples, double smFr ) {
   
   double mean = cnvt::getMean( samples );
   double std  = cnvt::getSTD( samples, mean );
   const double sF = smFr * std;
   const vector<double>::size_type N = samples.size();

   assert( N > 0.0 );

   x = cnvt::linSpaceToVec( mean - PLOTTING_HALF_WIDTH_IN_STD * std, mean + PLOTTING_HALF_WIDTH_IN_STD * std, numBins );

   for( size_t i = 0; i < numBins; i ++ ) {
      
      double v = 0.0;
      
      for( vector<double>::size_type j = 0; j < N; j ++ ) {
         
         v += pdfSmoothing( ( x[i]-samples[j] )/sF )/sF;
      }
      y.push_back( v/( double )N );
   }

   assert( x.size() == y.size() );
   assert( numBins == y.size() );

   return;
}

ProbDist & ProbDist::getEqualMixture( const vector<const ProbDist *> & ps ) {
   assert( ps.size() > 1 );

   const unsigned n = ps.size();
   const unsigned N = ps[0]->getNumberOfSimPoints();

   for( unsigned i = 1; i < n; i ++ ) {
      if( ps[i]->getNumberOfSimPoints() != N ) {
         assert( false );
      }
   }

   double * mixture = new double[n*N];

   for( unsigned i = 0; i < n; i ++ ) {
      for( unsigned j = 0; j < N; j ++ ) {
         
         mixture[i*N+j] = ps[i]->getSimPoint( j );
      }
   }

   return *( new ProbDist( mixture,N*n ) );
}

ProbDist * ProbDist::createAddMaxProbDist( const vector<ProbDist *> & pds1, const vector<ProbDist *> & pds2, vector<ProbDist *> & sumpds ) {
   assert( pds1.size() == pds2.size() );
   assert( sumpds.size() == 0 );

   for( unsigned i = 0; i < pds1.size(); i ++ )
      sumpds.push_back( &( *pds1[i] + *pds2[i] ) );

   ProbDist * rst = ProbDist::createMaxProbDist( sumpds );

   return rst;
}

ProbDist * ProbDist::createMaxProbDist
( vector<unsigned> & slctV, const vector<ProbDist *> & pds ) {
   //assert( pds.size() > 1 );
   assert( slctV.size() == ( vector<unsigned>::size_type )0 );

   unsigned NN = pds[0]->getNumberOfSimPoints();
   double * tmp = new double[NN];

   for( unsigned i = 1; i < pds.size(); i ++ )
      if( NN != pds[i]->getNumberOfSimPoints() ) assert( false );

   for( unsigned k = 0; k < NN; k ++ ) {
      unsigned select;

      tmp[k] = pds[0]->getSimPoint( k );
      select = 0;

      for( unsigned i = 1; i < pds.size(); i ++ )
         if( pds[i]->getSimPoint( k ) >= tmp[k] ) {
            tmp[k] = pds[i]->getSimPoint( k );
            select = i;
         }

      slctV.push_back( select );
   }

   assert( slctV.size() == NN );

   return new ProbDist( tmp, NN );
}

ProbDist * ProbDist::createMaxProbDistwithCriticality
( vector<double> & slctV, const vector<ProbDist *> & pds ) {
   //assert( pds.size() > 1 );
   assert( slctV.size() == pds.size() );

   unsigned NN = pds[0]->getNumberOfSimPoints();
   double * tmp = new double[NN];

   for( unsigned i = 1; i < pds.size(); i ++ )
      if( NN != pds[i]->getNumberOfSimPoints() )
         assert( false );

   for( unsigned k = 0; k < NN; k ++ ) {
      unsigned select;

      tmp[k] = pds[0]->getSimPoint( k );
      select = 0;

      for( unsigned i = 1; i < pds.size(); i ++ )
         if( pds[i]->getSimPoint( k ) >= tmp[k] ) {
            tmp[k] = pds[i]->getSimPoint( k );
            select = i;
         }

      slctV[select] ++;
   }
   for( unsigned i=0; i<slctV.size(); i++ )
      slctV[i] = slctV[i]/NN;

   return new ProbDist( tmp, NN );
}

ProbDist * ProbDist::createLinCom
( const ProbDist * pd, double f1,
  const vector<ProbDist *> & pds, double f2 ) {
   const unsigned N = pd->getNumberOfSimPoints();

   for( unsigned i = 0; i < pds.size(); i ++ )
      assert( pds[i]->getNumberOfSimPoints() == N );

   double * sm = new double[N];

   for( unsigned i = 0; i < N; i ++ ) {
      sm[i] = pd->sim[i];

      for( unsigned j = 0; j < pds.size(); j ++ )
         sm[i] += pds[j]->sim[i];
   }

   return new ProbDist( sm,N );
}

ostream & ProbDist::matlabToOstream
( ostream & os, const vector<string> & names,
  const vector<ProbDist *> & p1, const vector<ProbDist *> & p2,
  const vector<ProbDist *> & ap1, const vector<ProbDist *> & ap2,
  const vector<double> & ovs1, const vector<double> & ovs2,
  const string & s1, const string & s2,
  const string & kind, double kappa ) {
   if( kind == "first" )
      return matlabToOstreamFirstKind( os,names,p1,p2,ovs1,ovs2,s1,s2,kappa );
   if( kind == "second" )
      return matlabToOstreamSecondKind( os,names,p1,p2,ovs1,ovs2,s1,s2,kappa );
   if( kind == "third" )
      return matlabToOstreamThirdKind( os,names,p1,p2,ap1,ap2,ovs1,ovs2,s1,s2,kappa );

   assert( false );
   return os;
}

ostream & ProbDist::matlabToOstream
( ostream & os, const vector<string> & names,
  const vector<ProbDist *> & p1, const vector<ProbDist *> & p2,
  const vector<double> & ovs1, const vector<double> & ovs2,
  const string & s1, const string & s2,
  const string & kind, double kappa ) {
   if( kind == "first" )
      return matlabToOstreamFirstKind( os,names,p1,p2,ovs1,ovs2,s1,s2,kappa );
   if( kind == "second" )
      return matlabToOstreamSecondKind( os,names,p1,p2,ovs1,ovs2,s1,s2,kappa );
   if( kind == "third" )
      assert( false );
   //return matlabToOstreamThirdKind(os,names,p1,p2,ap1,ap2,ovs1,ovs2,s1,s2,kappa);

   assert( false );
   return os;
}

ostream & ProbDist::matlabToOstreamFirstKind
( ostream & os, const vector<string> & names,
  const vector<ProbDist *> & p1, const vector<ProbDist *> & p2,
  const vector<double> & ov1, const vector<double> & ov2,
  const string & s1, const string & s2, double kappa ) {
   unsigned n = names.size();
   assert( n == p1.size() && n == p2.size() );
   assert( n == ov1.size() && n == ov2.size() );

   os << "figure;" << endl;
   os << endl;

   if( n == 1 ) {
      os << "subplot(211);" << endl;
      matlabToOstream( os,names[0],*p1[0],*p2[0],ov1[0],ov2[0],s1,s2,kappa,true );
      os << "subplot(212);" << endl;
      matlabToOstream( os,names[0],*p1[0],*p2[0],ov1[0],ov2[0],s1,s2,kappa,false );
      return os;
   }

   for( unsigned i = 0; i < n; i ++ ) {
      os << "subplot(" << n << ",2," << 2*i+1 << ");" << endl;
      matlabToOstream( os,names[i],*p1[i],*p2[i],ov1[i],ov2[i],s1,s2,kappa,true );
      os << "subplot(" << n << ",2," << 2*i+2 << " );" << endl;
      matlabToOstream( os,names[i],*p1[i],*p2[i],ov1[i],ov2[i],s1,s2,kappa,false );
   }

   return os;
}

ostream & ProbDist::matlabToOstream
( ostream & os, const string & name, ProbDist & p1, ProbDist & p2,
  double ov1, double ov2,
  const string & s1, const string & s2, double kappa, bool cdf ) {
   os << "clear;" << endl;

   double xt1 = p1.getPercentilePoint( kappa );
   double xt2 = p2.getPercentilePoint( kappa );
   double xs1 = p1.getSTD();
   double xs2 = p2.getSTD();
   double xm1 = p1.getMean();
   double xm2 = p2.getMean();
   double yt1 = cdf? kappa:p1.getPDF( xt1 );
   double yt2 = cdf? kappa:p2.getPDF( xt2 );
   double ym1 = cdf? p1.getCDF( xm1 ):p1.getPDF( xm1 );
   double ym2 = cdf? p2.getCDF( xm2 ):p2.getPDF( xm2 );

   Mat::arrayToOstream( os,p1.getX(),p1.isByDist()?numBins:p1.N,"X1" );
   if( cdf ) Mat::arrayToOstream( os,p1.getCDF(),p1.isByDist()?numBins:p1.N,"Y1" );
   else Mat::arrayToOstream( os,p1.getPDF(),p1.isByDist()?numBins:p1.N,"Y1" );
   Mat::arrayToOstream( os,p2.getX(),p2.isByDist()?numBins:p2.N,"X2" );
   if( cdf ) Mat::arrayToOstream( os,p2.getCDF(),p2.isByDist()?numBins:p2.N,"Y2" );
   else Mat::arrayToOstream( os,p2.getPDF(),p2.isByDist()?numBins:p2.N,"Y2" );

   os << "plot(X1,Y1,'r-',X2,Y2,'b-.');" << endl;
   os << "ax=axis;" << endl;
   os << "line([ax(1) " << xt1 << " " << xt1 << "],[1 1 0]*" << yt1
      << ",'Color','r','LineStyle','-');" << endl;
   os << "line([ax(1) " << xt2 << " " << xt2 << "],[1 1 0]*" << yt2
      << ",'Color','b','LineStyle','-.');" << endl;
   os << "line([ax(1) " << xm1 << " " << xm1 << "],[1 1 0]*" << ym1
      << ",'Color','r','LineStyle','-');" << endl;
   os << "line([ax(1) " << xm2 << " " << xm2 << "],[1 1 0]*" << ym2
      << ",'Color','b','LineStyle','-.');" << endl;
   os << endl;

   if( cdf ) os << "axis( [ax(1:2) 0 1.1] );" << endl << endl;

   os << "title( '" << name << "' );" << endl;
   if( cdf ) os << "ylabel('cdf')" << endl;
   else os << "ylabel('pdf')" << endl;

   if( cdf )
      os << "xlabel('\\mu_{" << s1 << "}=" << xm1 << ", "
         << "\\sigma_{" << s1 << "}=" << xs1 << ", "
         << "t" << ( unsigned )( kappa*100.0+.1 ) << "_{" << s1 << "}=" << xt1 << ", "
         << "and t" << ( unsigned )( kappa*100.0+.1 ) << "_{" << s1 << ",approx}="
         << ov1 << "');" << endl;
   else
      os << "xlabel('\\mu_{" << s2 << "}=" << xm2 << ", "
         << "\\sigma_{" << s2 << "}=" << xs2 << ", "
         << "t" << ( unsigned )( kappa*100.0+.1 ) << "_{" << s2 << "}=" << xt2 << ", "
         << "and nominal=" << ov2
         << "');" << endl;
   os << "legend('" << s1 << "','" << s2 << "');" << endl;
   os << endl;

   return os;
}

ostream & ProbDist::matlabToOstreamSecondKind
( ostream & os, const vector<string> & names,
  const vector<ProbDist *> & p1, const vector<ProbDist *> & p2,
  const vector<double> & ovs1, const vector<double> & ovs2,
  const string & s1, const string & s2, double kappa ) {
   unsigned n = names.size();
   assert( n == p1.size() && n == p2.size() );

   os << "figure;" << endl;
   os << endl;

   os << "subplot(221);" << endl;
   os << "title('cdf of " << s1 << " ');" << endl;
   matlabToOstream( os, names, p1, true, kappa );

   os << "subplot(222);" << endl;
   os << "title('pdf of " << s1 << " ');" << endl;
   matlabToOstream( os, names, p1, false, kappa );

   os << "subplot(223);" << endl;
   os << "title('cdf of " << s2 << " ');" << endl;
   matlabToOstream( os, names, p2, true, kappa );

   os << "subplot(224);" << endl;
   os << "title('pdf of " << s2 << " ');" << endl;
   matlabToOstream( os, names, p2, false, kappa );

   return os;
}

ostream & ProbDist::matlabToOstream
( ostream & os,
  const vector<string> & ns, const vector<ProbDist *> & ps,
  bool cdf, double aph ) {
   static const unsigned nc = 7;
   static const string cls[] = { "b", "r", "k", "c", "m", "y", "g" };
   static const unsigned nl = 4;
   static const string lss[] = { "-", "-.", "--", ":" };

   unsigned n = ns.size();
   assert( n > 0 );
   assert( n == ps.size() );

   os << "hold on;" << endl;
   for( unsigned i = 0; i < n; i ++ )
      matlabToOstream( os,*ps[i],cdf,aph,cls[i-( i/nc )*nc],lss[i-( i/nl )*nl],false );

   os << "legend('" << ns[0] << "'";
   for( unsigned i = 1; i < n; i ++ )
      os << ",'" << ns[i] << "'";
   os << ");" << endl;

   for( unsigned i = 0; i < n; i ++ )
      matlabToOstream( os,*ps[i],cdf,aph,cls[i-( i/nc )*nc],lss[i-( i/nl )*nl],true );

   if( cdf ) os << "ax=axis; axis( [ax(1:2) 0 1.1] );" << endl;
   os << "hold off;" << endl;

   return os;
}

ostream & ProbDist::matlabToOstream
( ostream & os, ProbDist & p1, bool cdf, double kappa,
  const string & clr, const string & ls, bool lineD ) {
   os << "clear;" << endl;

   double xt1 = p1.getPercentilePoint( kappa );
   double xs1 = p1.getSTD();
   double xm1 = p1.getMean();
   double yt1 = cdf? kappa:p1.getPDF( xt1 );
   double ym1 = cdf? p1.getCDF( xm1 ):p1.getPDF( xm1 );

   if( !lineD ) {
      Mat::arrayToOstream( os,p1.getX(),p1.isByDist()?numBins:p1.N,"X1" );
      if( cdf ) Mat::arrayToOstream( os,p1.getCDF(),p1.isByDist()?numBins:p1.N,"Y1" );
      else Mat::arrayToOstream( os,p1.getPDF(),p1.isByDist()?numBins:p1.N,"Y1" );
      os << "plot(X1,Y1,'" << clr << ls << "');" << endl;
      os << "ax=axis;" << endl;

      return os;
   }

   os << "line(" << xt1 << "*[1 1],[1 0]*" << yt1
      << ",'Color','" << clr << "','LineStyle','" << ls << "');" << endl;
   os << "line(" << xm1 << "*[1 1],[1 0]*" << ym1
      << ",'Color','" << clr << "','LineStyle','" << ls << "');" << endl;
   os << endl;

   return os;
}

ostream & ProbDist::matlabToOstreamThirdKind
( ostream & os, const vector<string> & names,
  const vector<ProbDist *> & p1, const vector<ProbDist *> & p2,
  const vector<ProbDist *> & ap1, const vector<ProbDist *> & ap2,
  const vector<double> & ovs1, const vector<double> & ovs2,
  const string & s1, const string & s2, double p ) {
   unsigned n = names.size();
   assert( n == p1.size() && n == p2.size() );
   assert( n == ap1.size() && n == ap2.size() );
   assert( n == ovs1.size() && n == ovs2.size() );

   os << "figure;" << endl;
   os << endl;

   os << "subplot(311);" << endl;
   os << "title('" << unsigned( p*100.0+.1 )
      << "\% trust intervals of " << s1 << "');" << endl;
   matlabToOstream( os, names, p1, ap1, ovs1, p );
   os << "ax1=axis;" << endl;

   os << "subplot(312);" << endl;
   os << "title('" << unsigned( p*100.0+.1 )
      << "\% trust intervals of " << s2 << "');" << endl;
   matlabToOstream( os, names, p2, ap2, ovs2, p );
   os << "ax2=axis;" << endl << endl;

   os << "ax=[min(ax1(1),ax2(1)) max(ax1(2),ax2(2)) "
      << "min(ax1(3),ax2(3)) max(ax1(4),ax2(4))];" << endl;
   os << "subplot(311); axis(ax); subplot(312); axis(ax);" << endl << endl;

   os << "subplot(313);" << endl;
   matlabToOstream( os, p1, p2, ap1, ap2, s1, s2 );
   os << "title('\\sigma/\\mu');" << endl;
   os << "axt=axis;axis([ax(1:2) axt(3:4)]);" << endl << endl;

   return os;
}

ostream & ProbDist::matlabToOstream( ostream & os,
                                     const vector<string> & names,
                                     const vector<ProbDist *> & ps, const vector<ProbDist *> & aps,
                                     const vector<double> & ovs, double p ) {
   const double xp = getNormInv( p );
   const unsigned n = names.size();
   double m, s, t, pm;
   unsigned num = 0;
   bool wasA = true;

   assert( n == ps.size() );

   for( unsigned i = 0; i < n; ) {
      ProbDist * pb;
      if( wasA ) {
         pb = ps[i];
         wasA = false;
         num ++;
      } else if( aps[i] != NULL ) {
         pb = aps[i];
         wasA = true;
         i++;
         num ++;
      } else {
         i ++;
         wasA = true;
         continue;
      }

      m = pb->getMean();
      s = pb->getSTD();
      t = pb->getPercentilePoint( p );
      os << "line([1 1]*" <<num<< "," <<m<< "+[-1 1]*" <<s*xp<< ");" << endl;
      os << "line([-.1 .1]+" << num << "," << ( m+s*xp ) << "*[1 1]);" << endl;
      os << "line([-.1 .1]+" << num << "," << ( m-s*xp ) << "*[1 1]);" << endl;

      // optimal values
      if( !wasA )
         os << "line(.2*[-1 1]+" << num << "," << ovs[i] << "*[1 1],"
            << "'Color','k');" << endl;

      // p% point
      os << "line(.15*[-1 1]+" << num << "," << t << "*[1 1],"
         << "'Color','r');" << endl;

      os << "text(" << num << "," << ( m-s*xp*1.1 ) << ","
         << "'" << ( wasA? ( names[i-1]+"+D" ):names[i] ) << "',"
         << "'HorizontalAlignment','center','VerticalAlignment','top');"
         << endl;

      /*
      os << "text(" << num << ",0,"// << (m-s*xp*1.1-10) << ","
         << "'" << cnvt::doubleToString(s/m,2) << "',"
         << "'HorizontalAlignment','center','VerticalAlignment','top');"
         << endl;
      */

      if( num != 1 )
         os << "line([-1 0]+" << num << ","
            << "[" << pm << " " << m << "]);" << endl;

      pm = m;
   }

   return os;
}

ostream & ProbDist::matlabToOstream( ostream & os,
                                     const vector<ProbDist *> & ps1, const vector<ProbDist *> & ps2,
                                     const vector<ProbDist *> & aps1, const vector<ProbDist *> & aps2,
                                     const string & s1, const string & s2 ) {
   const unsigned n = ps1.size();
   unsigned num = 0;
   bool wasA = true;

   for( unsigned i = 0; i < n; ) {
      ProbDist * pb1, * pb2;
      if( wasA ) {
         pb1 = ps1[i];
         pb2 = ps2[i];
         wasA = false;
         num ++;
      } else if( aps1[i] != NULL ) {
         pb1 = aps1[i];
         pb2 = aps2[i];
         wasA = true;
         i++;
         num ++;
      } else {
         i ++;
         wasA = true;
         continue;
      }

      os << "MS(1," << num << ")=" << pb1->getSTD()/pb1->getMean() << ";" << endl;
      os << "MS(2," << num << ")=" << pb2->getSTD()/pb2->getMean() << ";" << endl;
   }

   os << "plot(1:size(MS,2),MS(1,:),'o',1:size(MS,2),MS(2,:),'x');" << endl;
   os << "legend('" << s1 << "','" << s2 << "');" << endl;

   return os;
}

void ProbDist::getPDFCDF
( double * pdf, double * cdf,
  const double * x, unsigned num, const double * sim, unsigned N, double std ) {
   assert( num > 0 );
   assert( N > 0 );

   double smoothingF = plottingSmoothingFactor * std;

   // start
   double s = clock();

   for( size_t i = 0; i < num; i ++ ) {
      pdf[i] = 0.0;
      cdf[i] = 0.0;

      for( size_t j = 0; j < N; j ++ ) {
         pdf[i] += ProbDist::pdfSmoothing( ( x[i]-sim[j] )/smoothingF )/smoothingF;
         cdf[i] += ProbDist::cdfSmoothing( ( x[i]-sim[j] )/smoothingF );
      }

      pdf[i] /= ( double )N;
      cdf[i] /= ( double )N;
   }

   // time it!
   double e = clock();

   double timeInSeconds = ( e-s )*1e-6;

   cout << "Smoothing pdf and cdf for plotting took " << timeInSeconds
        << cnvt::addS( " second", timeInSeconds ) << "." << endl;

   return;
}

const double ProbDist::norminv_precision = 1e-4;
const double ProbDist::norminvN = 5000;
const double ProbDist::norminv[]
= {
   0.00000000000000000000e+00,
   2.50662830088085961805e-04,
   5.01325675925498571127e-04,
   7.51988553262405924789e-04,
   1.00265147784815537857e-03,
   1.25331446543239352805e-03,
   1.50397753176507260539e-03,
   1.75464069259534480999e-03,
   2.00530396367351766707e-03,
   2.25596736074883119638e-03,
   2.50663089957169939181e-03,
   2.75729459589175779008e-03,
   3.00795846545927249988e-03,
   3.25862252402374678525e-03,
   3.50928678733588433891e-03,
   3.75995127114592004453e-03,
   4.01061599120390663981e-03,
   4.26128096326028067004e-03,
   4.51194620306586899328e-03,
   4.76261172637105524574e-03,
   5.01327754892663159103e-03,
   5.26394368648379611803e-03,
   5.51461015479332884726e-03,
   5.76527696960671583171e-03,
   6.01594414667531215274e-03,
   6.26661170175035753260e-03,
   6.51727965058409176163e-03,
   6.76794800892753598692e-03,
   7.01861679253328301503e-03,
   7.26928601715355442170e-03,
   7.51995569854049458747e-03,
   7.77062585244699295661e-03,
   8.02129649462588259490e-03,
   8.27196764083020126546e-03,
   8.52263930681293468972e-03,
   8.77331150832812677043e-03,
   9.02398426112923160436e-03,
   9.27465758096993921067e-03,
   9.52533148360474452021e-03,
   9.77600598478812338188e-03,
   1.00266811002748153225e-02,
   1.02773568458198270165e-02,
   1.05280332371784478979e-02,
   1.07787102901059656662e-02,
   1.10293880203588007954e-02,
   1.12800664436928377299e-02,
   1.15307455758650884842e-02,
   1.17814254326312241317e-02,
   1.20321060297488846569e-02,
   1.22827873829757829027e-02,
   1.25334695080693801772e-02,
   1.27841524207877813707e-02,
   1.30348361368894122975e-02,
   1.32855206721330769415e-02,
   1.35362060422782037872e-02,
   1.37868922630840270299e-02,
   1.40375793503110090493e-02,
   1.42882673197185852687e-02,
   1.45389561870676951166e-02,
   1.47896459681196822122e-02,
   1.50403366786357271107e-02,
   1.52910283343776938481e-02,
   1.55417209511081559625e-02,
   1.57924145445898118922e-02,
   1.60431091305855352824e-02,
   1.62938047248591677540e-02,
   1.65445013431747313393e-02,
   1.67951990012964215426e-02,
   1.70458977149891589831e-02,
   1.72965975000188947053e-02,
   1.75472983721506603505e-02,
   1.77980003471516282088e-02,
   1.80487034407880719833e-02,
   1.82994076688275872367e-02,
   1.85501130470379881066e-02,
   1.88008195911876091477e-02,
   1.90515273170452810458e-02,
   1.93022362403800808173e-02,
   1.95529463769624559100e-02,
   1.98036577425622674353e-02,
   2.00543703529507538752e-02,
   2.03050842238991433031e-02,
   2.05557993711800515713e-02,
   2.08065158105658308541e-02,
   2.10572335578296659930e-02,
   2.13079526287453385747e-02,
   2.15586730390874697916e-02,
   2.18093948046304414445e-02,
   2.20601179411500751548e-02,
   2.23108424644225117328e-02,
   2.25615683902247836368e-02,
   2.28122957343336908720e-02,
   2.30630245125277959228e-02,
   2.33137547405854392291e-02,
   2.35644864342861685980e-02,
   2.38152196094093306089e-02,
   2.40659542817363292233e-02,
   2.43166904670475275685e-02,
   2.45674281811253981955e-02,
   2.48181674397519140551e-02,
   2.50689082587111783385e-02,
   2.53196506537862568720e-02,
   2.55703946407623457227e-02,
   2.58211402354247623880e-02,
   2.60718874535592441688e-02,
   2.63226363109525518524e-02,
   2.65733868233927056357e-02,
   2.68241390066673267289e-02,
   2.70748928765653755490e-02,
   2.73256484488767770191e-02,
   2.75764057393916954541e-02,
   2.78271647639015753950e-02,
   2.80779255381983679218e-02,
   2.83286880780745167763e-02,
   2.85794523993237736814e-02,
   2.88302185177404315941e-02,
   2.90809864491195606273e-02,
   2.93317562092570149890e-02,
   2.95825278139491970597e-02,
   2.98333012789935882181e-02,
   3.00840766201890576215e-02,
   3.03348538533344570800e-02,
   3.05856329942294710711e-02,
   3.08364140586754667539e-02,
   3.10871970624735302624e-02,
   3.13379820214264581679e-02,
   3.15887689513376021533e-02,
   3.18395578680115073911e-02,
   3.20903487872529827318e-02,
   3.23411417248677598990e-02,
   3.25919366966630000282e-02,
   3.28427337184467524334e-02,
   3.30935328060271566342e-02,
   3.33443339752143713683e-02,
   3.35951372418186039459e-02,
   3.38459426216513176167e-02,
   3.40967501305251483035e-02,
   3.43475597842528498904e-02,
   3.45983715986492301742e-02,
   3.48491855895289373568e-02,
   3.51000017727089580477e-02,
   3.53508201640056196613e-02,
   3.56016407792375533248e-02,
   3.58524636342235775155e-02,
   3.61032887447837458339e-02,
   3.63541161267394372092e-02,
   3.66049457959124260875e-02,
   3.68557777681263257219e-02,
   3.71066120592044093596e-02,
   3.73574486849723580439e-02,
   3.76082876612560193519e-02,
   3.78591290038825870057e-02,
   3.81099727286805453619e-02,
   3.83608188514791906276e-02,
   3.86116673881085545328e-02,
   3.88625183544003133251e-02,
   3.91133717661869620419e-02,
   3.93642276393020226766e-02,
   3.96150859895795723342e-02,
   3.98659468328561791828e-02,
   4.01168101849681060789e-02,
   4.03676760617535657083e-02,
   4.06185444790513258684e-02,
   4.08694154527020972467e-02,
   4.11202889985466391032e-02,
   4.13711651324276327713e-02,
   4.16220438701886547017e-02,
   4.18729252276744470795e-02,
   4.21238092207308623127e-02,
   4.23746958652046618043e-02,
   4.26255851769443347421e-02,
   4.28764771717992654310e-02,
   4.31273718656200316657e-02,
   4.33782692742583839141e-02,
   4.36291694135675645061e-02,
   4.38800722994011765943e-02,
   4.41309779476148772437e-02,
   4.43818863740655378258e-02,
   4.46327975946104182903e-02,
   4.48837116251088741326e-02,
   4.51346284814211837211e-02,
   4.53855481794091727976e-02,
   4.56364707349353471155e-02,
   4.58873961638635030624e-02,
   4.61383244820595186941e-02,
   4.63892557053897300334e-02,
   4.66401898497223049711e-02,
   4.68911269309261122262e-02,
   4.71420669648716650357e-02,
   4.73930099674306978819e-02,
   4.76439559544766175203e-02,
   4.78949049418835315350e-02,
   4.81458569455271712112e-02,
   4.83968119812846070404e-02,
   4.86477700650345332156e-02,
   4.88987312126563933301e-02,
   4.91496954400315877454e-02,
   4.94006627630425854125e-02,
   4.96516331975726532555e-02,
   4.99026067595075353833e-02,
   5.01535834647335795888e-02,
   5.04045633291390210440e-02,
   5.06555463686132259604e-02,
   5.09065325990467124062e-02,
   5.11575220363316360284e-02,
   5.14085146963619427085e-02,
   5.16595105950325775290e-02,
   5.19105097482400607012e-02,
   5.21615121718819740870e-02,
   5.24125178818576828443e-02,
   5.26635268940685574712e-02,
   5.29145392244162598994e-02,
   5.31655548888045198508e-02,
   5.34165739031388364655e-02,
   5.36675962833258746176e-02,
   5.39186220452737910436e-02,
   5.41696512048922898530e-02,
   5.44206837780924698733e-02,
   5.46717197807867899551e-02,
   5.49227592288896657169e-02,
   5.51738021383168450451e-02,
   5.54248485249853109491e-02,
   5.56758984048143501511e-02,
   5.59269517937237836680e-02,
   5.61780087076360276632e-02,
   5.64290691624739701449e-02,
   5.66801331741629069172e-02,
   5.69312007586296742190e-02,
   5.71822719318018854451e-02,
   5.74333467096095756643e-02,
   5.76844251079841122132e-02,
   5.79355071428583959237e-02,
   5.81865928301669999012e-02,
   5.84376821858463846304e-02,
   5.86887752258337946909e-02,
   5.89398719660689102140e-02,
   5.91909724224931044212e-02,
   5.94420766110487913680e-02,
   5.96931845476803210615e-02,
   5.99442962483337574153e-02,
   6.01954117289567325333e-02,
   6.04465310054986479371e-02,
   6.06976540939105566053e-02,
   6.09487810101454266509e-02,
   6.11999117701574335548e-02,
   6.14510463899026956880e-02,
   6.17021848853390661449e-02,
   6.19533272724263478493e-02,
   6.22044735671255510923e-02,
   6.24556237853999690612e-02,
   6.27067779432138178164e-02,
   6.29579360565341167311e-02,
   6.32090981413288149904e-02,
   6.34602642135682210034e-02,
   6.37114342892238227911e-02,
   6.39626083842691761649e-02,
   6.42137865146798630933e-02,
   6.44649686964330198569e-02,
   6.47161549455070039816e-02,
   6.49673452778830595733e-02,
   6.52185397095437213721e-02,
   6.54697382564730645527e-02,
   6.57209409346572459576e-02,
   6.59721477600845179756e-02,
   6.62233587487447566966e-02,
   6.64745739166293370115e-02,
   6.67257932797320763019e-02,
   6.69770168540480825836e-02,
   6.72282446555752116746e-02,
   6.74794767003117218485e-02,
   6.77307130042591881702e-02,
   6.79819535834202820501e-02,
   6.82331984538003533114e-02,
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   2.39544951682961571038e+00,
   2.39988998429141675572e+00,
   2.40437828259866170910e+00,
   2.40891554581546030178e+00,
   2.41350294958847610971e+00,
   2.41814171322273896436e+00,
   2.42283310188927858420e+00,
   2.42757842897478859356e+00,
   2.43237905858445024876e+00,
   2.43723640821009501778e+00,
   2.44215195157703313100e+00,
   2.44712722168415863777e+00,
   2.45216381405328887055e+00,
   2.45726339020543793623e+00,
   2.46242768138319467752e+00,
   2.46765849254068037055e+00,
   2.47295770662438707532e+00,
   2.47832728917097178112e+00,
   2.48376929325053552589e+00,
   2.48928586478724200859e+00,
   2.49487924829237917024e+00,
   2.50055179304905150772e+00,
   2.50630595979189552125e+00,
   2.51214432793045894243e+00,
   2.51806960337024543506e+00,
   2.52408462699198299362e+00,
   2.53019238385702749383e+00,
   2.53639601321495966602e+00,
   2.54269881939905317836e+00,
   2.54910428370618813432e+00,
   2.55561607737020501929e+00,
   2.56223807575215367649e+00,
   2.56897437388738447694e+00,
   2.57582930354890393687e+00,
   2.58280745200823957930e+00,
   2.58991368270156385734e+00,
   2.59715315803855517629e+00,
   2.60453136462719747612e+00,
   2.61205414122927948029e+00,
   2.61972770981024849490e+00,
   2.62755871010504282737e+00,
   2.63555423819034118083e+00,
   2.64372188963550103225e+00,
   2.65206980790219892796e+00,
   2.66060673878077169618e+00,
   2.66934209179252945887e+00,
   2.67828600965941010514e+00,
   2.68744944715147715542e+00,
   2.69684426087813067241e+00,
   2.70648331190425972537e+00,
   2.71638058346086408434e+00,
   2.72655131650440196722e+00,
   2.73701216648466827408e+00,
   2.74778138544499439533e+00,
   2.75887903454713789841e+00,
   2.77032723335217001548e+00,
   2.78215045378460690273e+00,
   2.79437586878105470589e+00,
   2.80703376834380513571e+00,
   2.82015805932015917179e+00,
   2.83378687004355800383e+00,
   2.84796328748791971464e+00,
   2.86273626350590326695e+00,
   2.87816173909547634580e+00,
   2.89430405305141880135e+00,
   2.91123772624300558576e+00,
   2.92904974893762615196e+00,
   2.94784255218492807771e+00,
   2.96773792534179170488e+00,
   2.98888226731579331741e+00,
   3.01145375849978735872e+00,
   3.03567236662708861417e+00,
   3.06181415176175564241e+00,
   3.09023230616782429436e+00,
   3.12138914935985223309e+00,
   3.15590675792179320425e+00,
   3.19465105376326530262e+00,
   3.23888011835299094443e+00,
   3.29052673149190688662e+00,
   3.35279478050486989815e+00,
   3.43161440362325143028e+00,
   3.54008379920611870872e+00,
   3.71901648545567731219e+00
};

const size_t ProbDist::numBins = 1001;

const double ProbDist::xinc = 0.005;

const double ProbDist::normx[]
= {
   -2.5,
   -2.4950000000000001066,
   -2.4900000000000002132,
   -2.4849999999999998757,
   -2.4799999999999999822,
   -2.4750000000000000888,
   -2.4700000000000001954,
   -2.4649999999999998579,
   -2.4599999999999999645,
   -2.4550000000000000711,
   -2.4500000000000001776,
   -2.4449999999999998401,
   -2.4399999999999999467,
   -2.4350000000000000533,
   -2.4300000000000001599,
   -2.4249999999999998224,
   -2.4199999999999999289,
   -2.4150000000000000355,
   -2.4100000000000001421,
   -2.4049999999999998046,
   -2.3999999999999999112,
   -2.3950000000000000178,
   -2.3900000000000001243,
   -2.3849999999999997868,
   -2.3799999999999998934,
   -2.375,
   -2.3700000000000001066,
   -2.3650000000000002132,
   -2.3599999999999998757,
   -2.3549999999999999822,
   -2.3500000000000000888,
   -2.3450000000000001954,
   -2.3399999999999998579,
   -2.3349999999999999645,
   -2.3300000000000000711,
   -2.3250000000000001776,
   -2.3199999999999998401,
   -2.3149999999999999467,
   -2.3100000000000000533,
   -2.3050000000000001599,
   -2.2999999999999998224,
   -2.2949999999999999289,
   -2.2900000000000000355,
   -2.2850000000000001421,
   -2.2799999999999998046,
   -2.2749999999999999112,
   -2.2700000000000000178,
   -2.2650000000000001243,
   -2.2599999999999997868,
   -2.2549999999999998934,
   -2.25,
   -2.2450000000000001066,
   -2.2400000000000002132,
   -2.2349999999999998757,
   -2.2299999999999999822,
   -2.2250000000000000888,
   -2.2199999999999997513,
   -2.2149999999999998579,
   -2.2099999999999999645,
   -2.2050000000000000711,
   -2.2000000000000001776,
   -2.1949999999999998401,
   -2.1899999999999999467,
   -2.1850000000000000533,
   -2.1800000000000001599,
   -2.1749999999999998224,
   -2.1699999999999999289,
   -2.1650000000000000355,
   -2.1600000000000001421,
   -2.1550000000000002487,
   -2.1499999999999999112,
   -2.1450000000000000178,
   -2.1400000000000001243,
   -2.1349999999999997868,
   -2.1299999999999998934,
   -2.125,
   -2.1200000000000001066,
   -2.1150000000000002132,
   -2.1099999999999998757,
   -2.1049999999999999822,
   -2.1000000000000000888,
   -2.0949999999999997513,
   -2.0899999999999998579,
   -2.0849999999999999645,
   -2.0800000000000000711,
   -2.0750000000000001776,
   -2.0699999999999998401,
   -2.0649999999999999467,
   -2.0600000000000000533,
   -2.0550000000000001599,
   -2.0499999999999998224,
   -2.0449999999999999289,
   -2.0400000000000000355,
   -2.0350000000000001421,
   -2.0300000000000002487,
   -2.0249999999999999112,
   -2.0200000000000000178,
   -2.0150000000000001243,
   -2.0099999999999997868,
   -2.0049999999999998934,
   -2,
   -1.9950000000000001066,
   -1.9899999999999999911,
   -1.9849999999999998757,
   -1.9799999999999999822,
   -1.9750000000000000888,
   -1.9699999999999999734,
   -1.9649999999999998579,
   -1.9599999999999999645,
   -1.9550000000000000711,
   -1.9499999999999999556,
   -1.9449999999999998401,
   -1.9399999999999999467,
   -1.9350000000000000533,
   -1.9300000000000001599,
   -1.9250000000000000444,
   -1.9199999999999999289,
   -1.9150000000000000355,
   -1.9100000000000001421,
   -1.9050000000000000266,
   -1.8999999999999999112,
   -1.8950000000000000178,
   -1.8900000000000001243,
   -1.8850000000000000089,
   -1.8799999999999998934,
   -1.875,
   -1.8700000000000001066,
   -1.8649999999999999911,
   -1.8599999999999998757,
   -1.8549999999999999822,
   -1.8500000000000000888,
   -1.8449999999999999734,
   -1.8399999999999998579,
   -1.8349999999999999645,
   -1.8300000000000000711,
   -1.8249999999999999556,
   -1.8199999999999998401,
   -1.8149999999999999467,
   -1.8100000000000000533,
   -1.8050000000000001599,
   -1.8000000000000000444,
   -1.7949999999999999289,
   -1.7900000000000000355,
   -1.7850000000000001421,
   -1.7800000000000000266,
   -1.7749999999999999112,
   -1.7700000000000000178,
   -1.7650000000000001243,
   -1.7600000000000000089,
   -1.7549999999999998934,
   -1.75,
   -1.7450000000000001066,
   -1.7399999999999999911,
   -1.7349999999999998757,
   -1.7299999999999999822,
   -1.7250000000000000888,
   -1.7199999999999999734,
   -1.7149999999999998579,
   -1.7099999999999999645,
   -1.7050000000000000711,
   -1.6999999999999999556,
   -1.6949999999999998401,
   -1.6899999999999999467,
   -1.6850000000000000533,
   -1.6800000000000001599,
   -1.6750000000000000444,
   -1.6699999999999999289,
   -1.6650000000000000355,
   -1.6600000000000001421,
   -1.6550000000000000266,
   -1.6499999999999999112,
   -1.6450000000000000178,
   -1.6400000000000001243,
   -1.6350000000000000089,
   -1.6299999999999998934,
   -1.625,
   -1.6200000000000001066,
   -1.6149999999999999911,
   -1.6099999999999998757,
   -1.6049999999999999822,
   -1.6000000000000000888,
   -1.5949999999999999734,
   -1.5899999999999998579,
   -1.5849999999999999645,
   -1.5800000000000000711,
   -1.5749999999999999556,
   -1.5699999999999998401,
   -1.5649999999999999467,
   -1.5600000000000000533,
   -1.5550000000000001599,
   -1.5500000000000000444,
   -1.5449999999999999289,
   -1.5400000000000000355,
   -1.5350000000000001421,
   -1.5300000000000000266,
   -1.5249999999999999112,
   -1.5200000000000000178,
   -1.5150000000000001243,
   -1.5100000000000000089,
   -1.5049999999999998934,
   -1.5,
   -1.4950000000000001066,
   -1.4899999999999999911,
   -1.4850000000000000977,
   -1.4799999999999999822,
   -1.4750000000000000888,
   -1.4699999999999999734,
   -1.4650000000000000799,
   -1.4599999999999999645,
   -1.4550000000000000711,
   -1.4499999999999999556,
   -1.4450000000000000622,
   -1.4399999999999999467,
   -1.4350000000000000533,
   -1.4299999999999999378,
   -1.4250000000000000444,
   -1.4199999999999999289,
   -1.4150000000000000355,
   -1.4099999999999999201,
   -1.4050000000000000266,
   -1.3999999999999999112,
   -1.3950000000000000178,
   -1.3899999999999999023,
   -1.3850000000000000089,
   -1.3799999999999998934,
   -1.375,
   -1.3700000000000001066,
   -1.3649999999999999911,
   -1.3600000000000000977,
   -1.3549999999999999822,
   -1.3500000000000000888,
   -1.3449999999999999734,
   -1.3400000000000000799,
   -1.3349999999999999645,
   -1.3300000000000000711,
   -1.3249999999999999556,
   -1.3200000000000000622,
   -1.3149999999999999467,
   -1.3100000000000000533,
   -1.3049999999999999378,
   -1.3000000000000000444,
   -1.2949999999999999289,
   -1.2900000000000000355,
   -1.2849999999999999201,
   -1.2800000000000000266,
   -1.2749999999999999112,
   -1.2700000000000000178,
   -1.2649999999999999023,
   -1.2600000000000000089,
   -1.2549999999999998934,
   -1.25,
   -1.2450000000000001066,
   -1.2399999999999999911,
   -1.2350000000000000977,
   -1.2299999999999999822,
   -1.2250000000000000888,
   -1.2199999999999999734,
   -1.2150000000000000799,
   -1.2099999999999999645,
   -1.2050000000000000711,
   -1.1999999999999999556,
   -1.1950000000000000622,
   -1.1899999999999999467,
   -1.1850000000000000533,
   -1.1799999999999999378,
   -1.1750000000000000444,
   -1.1699999999999999289,
   -1.1650000000000000355,
   -1.1599999999999999201,
   -1.1550000000000000266,
   -1.1499999999999999112,
   -1.1450000000000000178,
   -1.1399999999999999023,
   -1.1350000000000000089,
   -1.1299999999999998934,
   -1.125,
   -1.1200000000000001066,
   -1.1149999999999999911,
   -1.1100000000000000977,
   -1.1049999999999999822,
   -1.1000000000000000888,
   -1.0949999999999999734,
   -1.0900000000000000799,
   -1.0849999999999999645,
   -1.0800000000000000711,
   -1.0749999999999999556,
   -1.0700000000000000622,
   -1.0649999999999999467,
   -1.0600000000000000533,
   -1.0549999999999999378,
   -1.0500000000000000444,
   -1.0449999999999999289,
   -1.0400000000000000355,
   -1.0349999999999999201,
   -1.0300000000000000266,
   -1.0249999999999999112,
   -1.0200000000000000178,
   -1.0149999999999999023,
   -1.0100000000000000089,
   -1.0049999999999998934,
   -1,
   -0.99500000000000010658,
   -0.98999999999999999112,
   -0.9850000000000000977,
   -0.97999999999999998224,
   -0.97500000000000008882,
   -0.96999999999999997335,
   -0.96500000000000007994,
   -0.95999999999999996447,
   -0.95500000000000007105,
   -0.94999999999999995559,
   -0.94500000000000006217,
   -0.93999999999999994671,
   -0.93500000000000005329,
   -0.92999999999999993783,
   -0.92500000000000004441,
   -0.91999999999999992895,
   -0.91500000000000003553,
   -0.90999999999999992006,
   -0.90500000000000002665,
   -0.89999999999999991118,
   -0.89500000000000001776,
   -0.8899999999999999023,
   -0.88500000000000000888,
   -0.87999999999999989342,
   -0.875,
   -0.87000000000000010658,
   -0.86499999999999999112,
   -0.8600000000000000977,
   -0.85499999999999998224,
   -0.85000000000000008882,
   -0.84499999999999997335,
   -0.84000000000000007994,
   -0.83499999999999996447,
   -0.83000000000000007105,
   -0.82499999999999995559,
   -0.82000000000000006217,
   -0.81499999999999994671,
   -0.81000000000000005329,
   -0.80499999999999993783,
   -0.80000000000000004441,
   -0.79499999999999992895,
   -0.79000000000000003553,
   -0.78499999999999992006,
   -0.78000000000000002665,
   -0.77499999999999991118,
   -0.77000000000000001776,
   -0.7649999999999999023,
   -0.76000000000000000888,
   -0.75499999999999989342,
   -0.75,
   -0.74500000000000010658,
   -0.73999999999999999112,
   -0.7350000000000000977,
   -0.72999999999999998224,
   -0.72500000000000008882,
   -0.71999999999999997335,
   -0.71500000000000007994,
   -0.70999999999999996447,
   -0.70500000000000007105,
   -0.69999999999999995559,
   -0.69500000000000006217,
   -0.68999999999999994671,
   -0.68500000000000005329,
   -0.67999999999999993783,
   -0.67500000000000004441,
   -0.66999999999999992895,
   -0.66500000000000003553,
   -0.65999999999999992006,
   -0.65500000000000002665,
   -0.64999999999999991118,
   -0.64500000000000001776,
   -0.6399999999999999023,
   -0.63500000000000000888,
   -0.62999999999999989342,
   -0.625,
   -0.62000000000000010658,
   -0.61499999999999999112,
   -0.6100000000000000977,
   -0.60499999999999998224,
   -0.60000000000000008882,
   -0.59499999999999997335,
   -0.59000000000000007994,
   -0.58499999999999996447,
   -0.58000000000000007105,
   -0.57499999999999995559,
   -0.57000000000000006217,
   -0.56499999999999994671,
   -0.56000000000000005329,
   -0.55499999999999993783,
   -0.55000000000000004441,
   -0.54499999999999992895,
   -0.54000000000000003553,
   -0.53499999999999992006,
   -0.53000000000000002665,
   -0.52499999999999991118,
   -0.52000000000000001776,
   -0.5149999999999999023,
   -0.51000000000000000888,
   -0.50499999999999989342,
   -0.5,
   -0.49500000000000010658,
   -0.49000000000000021316,
   -0.48499999999999987566,
   -0.47999999999999998224,
   -0.47500000000000008882,
   -0.4700000000000001954,
   -0.46499999999999985789,
   -0.45999999999999996447,
   -0.45500000000000007105,
   -0.45000000000000017764,
   -0.44499999999999984013,
   -0.43999999999999994671,
   -0.43500000000000005329,
   -0.43000000000000015987,
   -0.42499999999999982236,
   -0.41999999999999992895,
   -0.41500000000000003553,
   -0.41000000000000014211,
   -0.4049999999999998046,
   -0.39999999999999991118,
   -0.39500000000000001776,
   -0.39000000000000012434,
   -0.38499999999999978684,
   -0.37999999999999989342,
   -0.375,
   -0.37000000000000010658,
   -0.36500000000000021316,
   -0.35999999999999987566,
   -0.35499999999999998224,
   -0.35000000000000008882,
   -0.3450000000000001954,
   -0.33999999999999985789,
   -0.33499999999999996447,
   -0.33000000000000007105,
   -0.32500000000000017764,
   -0.31999999999999984013,
   -0.31499999999999994671,
   -0.31000000000000005329,
   -0.30500000000000015987,
   -0.29999999999999982236,
   -0.29499999999999992895,
   -0.29000000000000003553,
   -0.28500000000000014211,
   -0.2799999999999998046,
   -0.27499999999999991118,
   -0.27000000000000001776,
   -0.26500000000000012434,
   -0.25999999999999978684,
   -0.25499999999999989342,
   -0.25,
   -0.24500000000000010658,
   -0.24000000000000021316,
   -0.23499999999999987566,
   -0.22999999999999998224,
   -0.22500000000000008882,
   -0.2200000000000001954,
   -0.21499999999999985789,
   -0.20999999999999996447,
   -0.20500000000000007105,
   -0.20000000000000017764,
   -0.19499999999999984013,
   -0.18999999999999994671,
   -0.18500000000000005329,
   -0.18000000000000015987,
   -0.17499999999999982236,
   -0.16999999999999992895,
   -0.16500000000000003553,
   -0.16000000000000014211,
   -0.1549999999999998046,
   -0.14999999999999991118,
   -0.14500000000000001776,
   -0.14000000000000012434,
   -0.13499999999999978684,
   -0.12999999999999989342,
   -0.125,
   -0.12000000000000010658,
   -0.11500000000000021316,
   -0.10999999999999987566,
   -0.10499999999999998224,
   -0.10000000000000008882,
   -0.095000000000000195399,
   -0.089999999999999857891,
   -0.084999999999999964473,
   -0.080000000000000071054,
   -0.075000000000000177636,
   -0.069999999999999840128,
   -0.064999999999999946709,
   -0.060000000000000053291,
   -0.055000000000000159872,
   -0.049999999999999822364,
   -0.044999999999999928946,
   -0.040000000000000035527,
   -0.035000000000000142109,
   -0.029999999999999804601,
   -0.024999999999999911182,
   -0.020000000000000017764,
   -0.015000000000000124345,
   -0.0099999999999997868372,
   -0.0049999999999998934186,
   0,
   0.0049999999999998934186,
   0.0099999999999997868372,
   0.015000000000000124345,
   0.020000000000000017764,
   0.024999999999999911182,
   0.029999999999999804601,
   0.035000000000000142109,
   0.040000000000000035527,
   0.044999999999999928946,
   0.049999999999999822364,
   0.055000000000000159872,
   0.060000000000000053291,
   0.064999999999999946709,
   0.069999999999999840128,
   0.075000000000000177636,
   0.080000000000000071054,
   0.084999999999999964473,
   0.089999999999999857891,
   0.095000000000000195399,
   0.10000000000000008882,
   0.10499999999999998224,
   0.10999999999999987566,
   0.11500000000000021316,
   0.12000000000000010658,
   0.125,
   0.12999999999999989342,
   0.13499999999999978684,
   0.14000000000000012434,
   0.14500000000000001776,
   0.14999999999999991118,
   0.1549999999999998046,
   0.16000000000000014211,
   0.16500000000000003553,
   0.16999999999999992895,
   0.17499999999999982236,
   0.18000000000000015987,
   0.18500000000000005329,
   0.18999999999999994671,
   0.19499999999999984013,
   0.20000000000000017764,
   0.20500000000000007105,
   0.20999999999999996447,
   0.21499999999999985789,
   0.2200000000000001954,
   0.22500000000000008882,
   0.22999999999999998224,
   0.23499999999999987566,
   0.24000000000000021316,
   0.24500000000000010658,
   0.25,
   0.25499999999999989342,
   0.25999999999999978684,
   0.26500000000000012434,
   0.27000000000000001776,
   0.27499999999999991118,
   0.2799999999999998046,
   0.28500000000000014211,
   0.29000000000000003553,
   0.29499999999999992895,
   0.29999999999999982236,
   0.30500000000000015987,
   0.31000000000000005329,
   0.31499999999999994671,
   0.31999999999999984013,
   0.32500000000000017764,
   0.33000000000000007105,
   0.33499999999999996447,
   0.33999999999999985789,
   0.3450000000000001954,
   0.35000000000000008882,
   0.35499999999999998224,
   0.35999999999999987566,
   0.36500000000000021316,
   0.37000000000000010658,
   0.375,
   0.37999999999999989342,
   0.38499999999999978684,
   0.39000000000000012434,
   0.39500000000000001776,
   0.39999999999999991118,
   0.4049999999999998046,
   0.41000000000000014211,
   0.41500000000000003553,
   0.41999999999999992895,
   0.42499999999999982236,
   0.43000000000000015987,
   0.43500000000000005329,
   0.43999999999999994671,
   0.44499999999999984013,
   0.45000000000000017764,
   0.45500000000000007105,
   0.45999999999999996447,
   0.46499999999999985789,
   0.4700000000000001954,
   0.47500000000000008882,
   0.47999999999999998224,
   0.48499999999999987566,
   0.49000000000000021316,
   0.49500000000000010658,
   0.5,
   0.50499999999999989342,
   0.50999999999999978684,
   0.51500000000000012434,
   0.52000000000000001776,
   0.52499999999999991118,
   0.5299999999999998046,
   0.53500000000000014211,
   0.54000000000000003553,
   0.54499999999999992895,
   0.54999999999999982236,
   0.55500000000000015987,
   0.56000000000000005329,
   0.56499999999999994671,
   0.56999999999999984013,
   0.57500000000000017764,
   0.58000000000000007105,
   0.58499999999999996447,
   0.58999999999999985789,
   0.5950000000000001954,
   0.60000000000000008882,
   0.60499999999999998224,
   0.60999999999999987566,
   0.61500000000000021316,
   0.62000000000000010658,
   0.625,
   0.62999999999999989342,
   0.63499999999999978684,
   0.64000000000000012434,
   0.64500000000000001776,
   0.64999999999999991118,
   0.6549999999999998046,
   0.66000000000000014211,
   0.66500000000000003553,
   0.66999999999999992895,
   0.67499999999999982236,
   0.68000000000000015987,
   0.68500000000000005329,
   0.68999999999999994671,
   0.69499999999999984013,
   0.70000000000000017764,
   0.70500000000000007105,
   0.70999999999999996447,
   0.71499999999999985789,
   0.7200000000000001954,
   0.72500000000000008882,
   0.72999999999999998224,
   0.73499999999999987566,
   0.74000000000000021316,
   0.74500000000000010658,
   0.75,
   0.75499999999999989342,
   0.75999999999999978684,
   0.76500000000000012434,
   0.77000000000000001776,
   0.77499999999999991118,
   0.7799999999999998046,
   0.78500000000000014211,
   0.79000000000000003553,
   0.79499999999999992895,
   0.79999999999999982236,
   0.80500000000000015987,
   0.81000000000000005329,
   0.81499999999999994671,
   0.81999999999999984013,
   0.82500000000000017764,
   0.83000000000000007105,
   0.83499999999999996447,
   0.83999999999999985789,
   0.8450000000000001954,
   0.85000000000000008882,
   0.85499999999999998224,
   0.85999999999999987566,
   0.86500000000000021316,
   0.87000000000000010658,
   0.875,
   0.87999999999999989342,
   0.88499999999999978684,
   0.89000000000000012434,
   0.89500000000000001776,
   0.89999999999999991118,
   0.9049999999999998046,
   0.91000000000000014211,
   0.91500000000000003553,
   0.91999999999999992895,
   0.92499999999999982236,
   0.93000000000000015987,
   0.93500000000000005329,
   0.93999999999999994671,
   0.94499999999999984013,
   0.95000000000000017764,
   0.95500000000000007105,
   0.95999999999999996447,
   0.96499999999999985789,
   0.9700000000000001954,
   0.97500000000000008882,
   0.97999999999999998224,
   0.98499999999999987566,
   0.99000000000000021316,
   0.99500000000000010658,
   1,
   1.0049999999999998934,
   1.0099999999999997868,
   1.0150000000000001243,
   1.0200000000000000178,
   1.0249999999999999112,
   1.0299999999999998046,
   1.0350000000000001421,
   1.0400000000000000355,
   1.0449999999999999289,
   1.0499999999999998224,
   1.0550000000000001599,
   1.0600000000000000533,
   1.0649999999999999467,
   1.0699999999999998401,
   1.0750000000000001776,
   1.0800000000000000711,
   1.0849999999999999645,
   1.0899999999999998579,
   1.0950000000000001954,
   1.1000000000000000888,
   1.1049999999999999822,
   1.1099999999999998757,
   1.1150000000000002132,
   1.1200000000000001066,
   1.125,
   1.1299999999999998934,
   1.1349999999999997868,
   1.1400000000000001243,
   1.1450000000000000178,
   1.1499999999999999112,
   1.1549999999999998046,
   1.1600000000000001421,
   1.1650000000000000355,
   1.1699999999999999289,
   1.1749999999999998224,
   1.1800000000000001599,
   1.1850000000000000533,
   1.1899999999999999467,
   1.1949999999999998401,
   1.2000000000000001776,
   1.2050000000000000711,
   1.2099999999999999645,
   1.2149999999999998579,
   1.2200000000000001954,
   1.2250000000000000888,
   1.2299999999999999822,
   1.2349999999999998757,
   1.2400000000000002132,
   1.2450000000000001066,
   1.25,
   1.2549999999999998934,
   1.2599999999999997868,
   1.2650000000000001243,
   1.2700000000000000178,
   1.2749999999999999112,
   1.2799999999999998046,
   1.2850000000000001421,
   1.2900000000000000355,
   1.2949999999999999289,
   1.2999999999999998224,
   1.3050000000000001599,
   1.3100000000000000533,
   1.3149999999999999467,
   1.3199999999999998401,
   1.3250000000000001776,
   1.3300000000000000711,
   1.3349999999999999645,
   1.3399999999999998579,
   1.3450000000000001954,
   1.3500000000000000888,
   1.3549999999999999822,
   1.3599999999999998757,
   1.3650000000000002132,
   1.3700000000000001066,
   1.375,
   1.3799999999999998934,
   1.3849999999999997868,
   1.3900000000000001243,
   1.3950000000000000178,
   1.3999999999999999112,
   1.4049999999999998046,
   1.4100000000000001421,
   1.4150000000000000355,
   1.4199999999999999289,
   1.4249999999999998224,
   1.4300000000000001599,
   1.4350000000000000533,
   1.4399999999999999467,
   1.4449999999999998401,
   1.4500000000000001776,
   1.4550000000000000711,
   1.4599999999999999645,
   1.4649999999999998579,
   1.4700000000000001954,
   1.4750000000000000888,
   1.4799999999999999822,
   1.4849999999999998757,
   1.4900000000000002132,
   1.4950000000000001066,
   1.5,
   1.5049999999999998934,
   1.5099999999999997868,
   1.5149999999999996803,
   1.5199999999999995737,
   1.5250000000000003553,
   1.5300000000000002487,
   1.5350000000000001421,
   1.5400000000000000355,
   1.5449999999999999289,
   1.5499999999999998224,
   1.5549999999999997158,
   1.5599999999999996092,
   1.5650000000000003908,
   1.5700000000000002842,
   1.5750000000000001776,
   1.5800000000000000711,
   1.5849999999999999645,
   1.5899999999999998579,
   1.5949999999999997513,
   1.5999999999999996447,
   1.6050000000000004263,
   1.6100000000000003197,
   1.6150000000000002132,
   1.6200000000000001066,
   1.625,
   1.6299999999999998934,
   1.6349999999999997868,
   1.6399999999999996803,
   1.6449999999999995737,
   1.6500000000000003553,
   1.6550000000000002487,
   1.6600000000000001421,
   1.6650000000000000355,
   1.6699999999999999289,
   1.6749999999999998224,
   1.6799999999999997158,
   1.6849999999999996092,
   1.6900000000000003908,
   1.6950000000000002842,
   1.7000000000000001776,
   1.7050000000000000711,
   1.7099999999999999645,
   1.7149999999999998579,
   1.7199999999999997513,
   1.7249999999999996447,
   1.7300000000000004263,
   1.7350000000000003197,
   1.7400000000000002132,
   1.7450000000000001066,
   1.75,
   1.7549999999999998934,
   1.7599999999999997868,
   1.7649999999999996803,
   1.7699999999999995737,
   1.7750000000000003553,
   1.7800000000000002487,
   1.7850000000000001421,
   1.7900000000000000355,
   1.7949999999999999289,
   1.7999999999999998224,
   1.8049999999999997158,
   1.8099999999999996092,
   1.8150000000000003908,
   1.8200000000000002842,
   1.8250000000000001776,
   1.8300000000000000711,
   1.8349999999999999645,
   1.8399999999999998579,
   1.8449999999999997513,
   1.8499999999999996447,
   1.8550000000000004263,
   1.8600000000000003197,
   1.8650000000000002132,
   1.8700000000000001066,
   1.875,
   1.8799999999999998934,
   1.8849999999999997868,
   1.8899999999999996803,
   1.8949999999999995737,
   1.9000000000000003553,
   1.9050000000000002487,
   1.9100000000000001421,
   1.9150000000000000355,
   1.9199999999999999289,
   1.9249999999999998224,
   1.9299999999999997158,
   1.9349999999999996092,
   1.9400000000000003908,
   1.9450000000000002842,
   1.9500000000000001776,
   1.9550000000000000711,
   1.9599999999999999645,
   1.9649999999999998579,
   1.9699999999999997513,
   1.9749999999999996447,
   1.9800000000000004263,
   1.9850000000000003197,
   1.9900000000000002132,
   1.9950000000000001066,
   2,
   2.0049999999999998934,
   2.0099999999999997868,
   2.0149999999999996803,
   2.0199999999999995737,
   2.0250000000000003553,
   2.0300000000000002487,
   2.0350000000000001421,
   2.0400000000000000355,
   2.0449999999999999289,
   2.0499999999999998224,
   2.0549999999999997158,
   2.0599999999999996092,
   2.0650000000000003908,
   2.0700000000000002842,
   2.0750000000000001776,
   2.0800000000000000711,
   2.0849999999999999645,
   2.0899999999999998579,
   2.0949999999999997513,
   2.0999999999999996447,
   2.1050000000000004263,
   2.1100000000000003197,
   2.1150000000000002132,
   2.1200000000000001066,
   2.125,
   2.1299999999999998934,
   2.1349999999999997868,
   2.1399999999999996803,
   2.1449999999999995737,
   2.1500000000000003553,
   2.1550000000000002487,
   2.1600000000000001421,
   2.1650000000000000355,
   2.1699999999999999289,
   2.1749999999999998224,
   2.1799999999999997158,
   2.1849999999999996092,
   2.1900000000000003908,
   2.1950000000000002842,
   2.2000000000000001776,
   2.2050000000000000711,
   2.2099999999999999645,
   2.2149999999999998579,
   2.2199999999999997513,
   2.2249999999999996447,
   2.2300000000000004263,
   2.2350000000000003197,
   2.2400000000000002132,
   2.2450000000000001066,
   2.25,
   2.2549999999999998934,
   2.2599999999999997868,
   2.2649999999999996803,
   2.2699999999999995737,
   2.2750000000000003553,
   2.2800000000000002487,
   2.2850000000000001421,
   2.2900000000000000355,
   2.2949999999999999289,
   2.2999999999999998224,
   2.3049999999999997158,
   2.3099999999999996092,
   2.3150000000000003908,
   2.3200000000000002842,
   2.3250000000000001776,
   2.3300000000000000711,
   2.3349999999999999645,
   2.3399999999999998579,
   2.3449999999999997513,
   2.3499999999999996447,
   2.3550000000000004263,
   2.3600000000000003197,
   2.3650000000000002132,
   2.3700000000000001066,
   2.375,
   2.3799999999999998934,
   2.3849999999999997868,
   2.3899999999999996803,
   2.3949999999999995737,
   2.4000000000000003553,
   2.4050000000000002487,
   2.4100000000000001421,
   2.4150000000000000355,
   2.4199999999999999289,
   2.4249999999999998224,
   2.4299999999999997158,
   2.4349999999999996092,
   2.4400000000000003908,
   2.4450000000000002842,
   2.4500000000000001776,
   2.4550000000000000711,
   2.4599999999999999645,
   2.4649999999999998579,
   2.4699999999999997513,
   2.4749999999999996447,
   2.4800000000000004263,
   2.4850000000000003197,
   2.4900000000000002132,
   2.4950000000000001066,
   2.5
};

const double ProbDist::normpdf[]
= {
   0.017528300493568540336,
   0.017748557513561032117,
   0.01797113295403963279,
   0.018196044690699273577,
   0.018423310646862048334,
   0.018652948792269904987,
   0.018884977141856162941,
   0.019119413754496220742,
   0.019356276731736964808,
   0.019595584216505323311,
   0.019837354391795312958,
   0.020081605479333991537,
   0.02032835573822584091,
   0.02057762346357607311,
   0.020829426985092186486,
   0.021083784665664118824,
   0.021340714899922785808,
   0.021600236112777133207,
   0.021862366757929387051,
   0.022127125316368685681,
   0.022394530294842899393,
   0.022664600224308894399,
   0.022937353658360692954,
   0.023212809171636133304,
   0.023490985358201366823,
   0.023771900829913806402,
   0.024055574214762971003,
   0.024342024155189535134,
   0.024631269306382506945,
   0.024923328334554323282,
   0.025218219915194382136,
   0.025515962731300342869,
   0.025816575471587690366,
   0.026120076828677393083,
   0.026426485497261724411,
   0.026735820172248226517,
   0.027048099546881785443,
   0.027363342310844956246,
   0.027681567148336572864,
   0.028002792736128583745,
   0.028327037741601189536,
   0.02865432082075626552,
   0.028984660616209415723,
   0.029318075755160256241,
   0.029654584847341278198,
   0.029994206482945311165,
   0.030336959230531639065,
   0.030682861634910817139,
   0.031031932215008273257,
   0.031384189461706644975,
   0.031739651835667417878,
   0.032098337765131206012,
   0.032460265643697444604,
   0.032825453828083162033,
   0.033193920635861122459,
   0.033565684343177547289,
   0.033940763182449214252,
   0.034319175340040225519,
   0.034700938953918819552,
   0.035086072111293865883,
   0.035474592846231424448,
   0.035866519137251744176,
   0.036261868904906222055,
   0.036660660009335266363,
   0.037062910247806474251,
   0.037468637352233810645,
   0.037877858986677483133,
   0.038290592744825449611,
   0.038706856147455608042,
   0.039126666639879972842,
   0.039550041589370227291,
   0.039976998282565137655,
   0.040407553922860307838,
   0.040841725627779809638,
   0.041279530426330417192,
   0.041720985256338612157,
   0.042166106961770311035,
   0.042614912290033758746,
   0.043067417889265741104,
   0.043523640305601241085,
   0.043983595980427198091,
   0.04444730124761994694,
   0.04491477233076709985,
   0.04538602534037398939,
   0.045861076271054894427,
   0.046339940998709215625,
   0.046822635277683162525,
   0.047309174737916737108,
   0.047799574882077033866,
   0.048293851082677308195,
   0.048792018579182770688,
   0.049294092475102836703,
   0.049800087735070774908,
   0.05031001918191051886,
   0.050823901493691162057,
   0.051341749200769455641,
   0.051863576682820565489,
   0.052389398165857643808,
   0.052919227719240319319,
   0.053453079252672043575,
   0.053990966513188062836,
   0.054532903082132377914,
   0.055078902372125766729,
   0.055628977624024120163,
   0.056183141903868048794,
   0.05674140809982401723,
   0.057303788919117130962,
   0.05787029688495622104,
   0.058440944333451476378,
   0.059015743410525248192,
   0.059594706068816075129,
   0.060177844064576421768,
   0.060765168954564782733,
   0.061356692092932485494,
   0.061952424628105143278,
   0.062552377499659972404,
   0.063156561435198654841,
   0.063764986947216648061,
   0.064377664329969344625,
   0.064994603656335220299,
   0.065615814774676595178,
   0.066241307305698729491,
   0.066871090639307143033,
   0.0675051739314641297,
   0.068143566101044591998,
   0.068786275826691903323,
   0.069433311543674172683,
   0.07008468144074131434,
   0.070740393456983394205,
   0.07140045527869101627,
   0.072064874336217998874,
   0.072733657800846701624,
   0.073406812581656918915,
   0.07408434532239832615,
   0.074766262398367616671,
   0.075452569913290204462,
   0.076143273696207353085,
   0.076838379298369091641,
   0.077537891990133986364,
   0.078241816757875115584,
   0.078950158300894149321,
   0.079662921028343006147,
   0.080380109056154169789,
   0.081101726203980234464,
   0.081827775992142817718,
   0.082558261638591631804,
   0.083293186055874463003,
   0.084032551848118308691,
   0.084776361308022241126,
   0.085524616413862636355,
   0.086277318826511517624,
   0.087034469886468332489,
   0.087796070610905635467,
   0.088562121690729453394,
   0.089332623487654999606,
   0.090107576031298097785,
   0.090886979016282884447,
   0.091670831799366345183,
   0.092459133396580683861,
   0.093251882480393524788,
   0.094049077376886947022,
   0.09485071606295540636,
   0.095656796163524016041,
   0.096467314948787075135,
   0.097282269331467469131,
   0.098101655864097817017,
   0.098925470736323725673,
   0.099753709772230081398,
   0.10058636842769055897,
   0.10142344178774106989,
   0.10226492456397803799,
   0.10311081109198141914,
   0.10396109532876419979,
   0.10481577085024761098,
   0.1056748308487636262,
   0.10653826813058507594,
   0.10740607511348379544,
   0.1082782438243178047,
   0.10915476589664740992,
   0.11003563256838166939,
   0.11092083467945554331,
   0.11181036266953775504,
   0.11270420657577059909,
   0.11360235603054232023,
   0.11450480025929235528,
   0.1154115280783499925,
   0.11632252789280711491,
   0.11723778769442601277,
   0.11815729505958227907,
   0.11908103714724369016,
   0.12000900069698558492,
   0.1209411720270431867,
   0.12187753703240178371,
   0.12281808118292524001,
   0.12376278952152314217,
   0.12471164666235723395,
   0.12566463678908815216,
   0.12662174365316269942,
   0.12758295057214188994,
   0.12854824042807100337,
   0.12951759566589174377,
   0.13049099829189736433,
   0.13146842987223106292,
   0.13244987153142792624,
   0.13343530395100233754,
   0.13442470736807907161,
   0.13541806157407129674,
   0.13641534591340345739,
   0.13741653928228178549,
   0.13842162012751113576,
   0.13943056644536028221,
   0.14044335578047473234,
   0.14145996522483880731,
   0.14248037141678648876,
   0.14350455054006241995,
   0.1445324783229328669,
   0.14556413003734761102,
   0.14659948049815274551,
   0.14763850406235576318,
   0.14868117462844201992,
   0.14972746563574487744,
   0.15077735006386791539,
   0.15183080043216171107,
   0.15288778879925371545,
   0.15394828676263372369,
   0.15501226545829321912,
   0.15607969556042083914,
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   0.13541806157407124123,
   0.13442470736807907161,
   0.13343530395100233754,
   0.132449871531427954,
   0.13146842987223097965,
   0.13049099829189736433,
   0.12951759566589174377,
   0.12854824042807100337,
   0.1275829505721419177,
   0.12662174365316278268,
   0.12566463678908823542,
   0.12471164666235713681,
   0.12376278952152307278,
   0.12281808118292524001,
   0.12187753703240178371,
   0.1209411720270431867,
   0.12000900069698565431,
   0.1190810371472437873,
   0.11815729505958236234,
   0.11723778769442594339,
   0.11632252789280704552,
   0.11541152807834995087,
   0.11450480025929235528,
   0.11360235603054232023,
   0.11270420657577059909,
   0.11181036266953779668,
   0.11092083467945564046,
   0.1100356325683816,
   0.10915476589664731277,
   0.10827824382431774919,
   0.10740607511348379544,
   0.10653826813058507594,
   0.1056748308487636262,
   0.10481577085024762486,
   0.1039610953287642553,
   0.10311081109198148853,
   0.1022649245639779686,
   0.10142344178774104213,
   0.10058636842769055897,
   0.099753709772230081398,
   0.098925470736323725673,
   0.098101655864097844773,
   0.09728226933146753852,
   0.09646731494878717228,
   0.095656796163523932774,
   0.094850716062955309216,
   0.094049077376886905388,
   0.093251882480393524788,
   0.092459133396580683861,
   0.091670831799366345183,
   0.090886979016282898325,
   0.090107576031298167174,
   0.089332623487654944094,
   0.088562121690729397883,
   0.087796070610905593834,
   0.087034469886468332489,
   0.086277318826511517624,
   0.085524616413862636355,
   0.084776361308022255003,
   0.084032551848118378079,
   0.08329318605587454627,
   0.082558261638591576292,
   0.081827775992142762207,
   0.081101726203980234464,
   0.080380109056154169789,
   0.079662921028343006147,
   0.078950158300894190955,
   0.078241816757875171096,
   0.077537891990134041875,
   0.076838379298369050008,
   0.076143273696207283696,
   0.075452569913290190584,
   0.074766262398367616671,
   0.07408434532239832615,
   0.073406812581656918915,
   0.072733657800846743258,
   0.072064874336218054385,
   0.071400455278690960759,
   0.070740393456983338694,
   0.070084681440741286584,
   0.069433311543674172683,
   0.068786275826691903323,
   0.068143566101044591998,
   0.067505173931464143577,
   0.066871090639307184667,
   0.066241307305698785002,
   0.065615814774676553545,
   0.064994603656335178665,
   0.064377664329969344625,
   0.063764986947216648061,
   0.063156561435198654841,
   0.06255237749966000016,
   0.061952424628105198789,
   0.061356692092932541005,
   0.060765168954564734161,
   0.060177844064576366256,
   0.059594706068816054312,
   0.059015743410525248192,
   0.058440944333451476378,
   0.05787029688495622104,
   0.057303788919117158718,
   0.056741408099824065803,
   0.056183141903867993283,
   0.055628977624024071591,
   0.055078902372125745912,
   0.054532903082132377914,
   0.053990966513188062836,
   0.053453079252672043575,
   0.052919227719240319319,
   0.05238939816585769238,
   0.051863576682820614061,
   0.051341749200769407069,
   0.050823901493691162057,
   0.05031001918191051886,
   0.049800087735070774908,
   0.049294092475102836703,
   0.048792018579182770688,
   0.048293851082677349829,
   0.047799574882077075499,
   0.047309174737916695475,
   0.04682263527768312783,
   0.046339940998709215625,
   0.045861076271054894427,
   0.04538602534037398939,
   0.04491477233076709985,
   0.04444730124761994694,
   0.043983595980427232786,
   0.043523640305601199452,
   0.043067417889265699471,
   0.042614912290033758746,
   0.042166106961770311035,
   0.041720985256338612157,
   0.041279530426330417192,
   0.040841725627779809638,
   0.040407553922860342532,
   0.039976998282565179288,
   0.039550041589370192596,
   0.039126666639879972842,
   0.038706856147455608042,
   0.038290592744825449611,
   0.037877858986677483133,
   0.037468637352233810645,
   0.037062910247806508945,
   0.036660660009335294118,
   0.0362618689049061943,
   0.035866519137251709481,
   0.035474592846231424448,
   0.035086072111293865883,
   0.034700938953918819552,
   0.034319175340040225519,
   0.033940763182449214252,
   0.033565684343177575044,
   0.033193920635861094703,
   0.032825453828083134278,
   0.032460265643697444604,
   0.032098337765131206012,
   0.031739651835667417878,
   0.031384189461706644975,
   0.031031932215008273257,
   0.030682861634910844895,
   0.03033695923053166682,
   0.029994206482945273001,
   0.029654584847341250442,
   0.029318075755160256241,
   0.028984660616209415723,
   0.02865432082075626552,
   0.028327037741601189536,
   0.028002792736128604562,
   0.027681567148336593681,
   0.027363342310844918082,
   0.027048099546881764627,
   0.026735820172248226517,
   0.026426485497261724411,
   0.026120076828677393083,
   0.025816575471587690366,
   0.025515962731300363686,
   0.02521821991519441683,
   0.024923328334554302466,
   0.024631269306382486128,
   0.024342024155189535134,
   0.024055574214762971003,
   0.023771900829913806402,
   0.023490985358201366823,
   0.023212809171636133304,
   0.02293735365836071724,
   0.022664600224308911747,
   0.022394530294842882046,
   0.022127125316368657926,
   0.021862366757929387051,
   0.021600236112777133207,
   0.021340714899922785808,
   0.021083784665664118824,
   0.020829426985092203833,
   0.020577623463576100865,
   0.020328355738225820093,
   0.020081605479333963782,
   0.019837354391795312958,
   0.019595584216505323311,
   0.019356276731736964808,
   0.019119413754496220742,
   0.018884977141856187227,
   0.018652948792269922335,
   0.018423310646862030987,
   0.018196044690699245822,
   0.01797113295403963279,
   0.017748557513561032117,
   0.017528300493568540336
};

const double ProbDist::normcdf[]
= {
   0.0062096653257761357317,
   0.0062978565085031303419,
   0.0063871547649431729618,
   0.0064775717318678533233,
   0.0065691191355467682539,
   0.0066618087919826998733,
   0.0067556526071406528683,
   0.0068506625771706528352,
   0.006946850788624319567,
   0.0070442294186650045162,
   0.0071428107352714213102,
   0.0072426070974346366121,
   0.007343630955348351072,
   0.0074458948505923983757,
   0.0075494114163092091233,
   0.0076541933773733254048,
   0.0077602535505536512223,
   0.0078676048446686061566,
   0.0079762602607337303867,
   0.0080862328921019552969,
   0.0081975359245961363502,
   0.0083101826366341041002,
   0.0084241863993456973098,
   0.0085395606766820054273,
   0.0086563190255165619463,
   0.0087744750957383689516,
   0.008894042630336782343,
   0.0090150354654779142616,
   0.0091374675305726793528,
   0.0092613528483361882288,
   0.0093867055348385748659,
   0.0095135397995469300758,
   0.0096418699453583427833,
   0.0097717103686240248256,
   0.0099030755591642538604,
   0.010035980100274063259,
   0.010170438668719689393,
   0.01030646603472541202,
   0.010444077061951089619,
   0.010583286707459794648,
   0.010724110021675817631,
   0.010866562148332698304,
   0.011010658324411393139,
   0.011156413880068247885,
   0.011303844238552801169,
   0.011452964916115240465,
   0.011603791521903543404,
   0.011756339757849980018,
   0.011910625418547078277,
   0.012066664391112744137,
   0.012224472655044706093,
   0.012384066282063841899,
   0.012545461435946571316,
   0.012708674372346032144,
   0.012873721438602027389,
   0.013040619073539627334,
   0.013209383807256299889,
   0.013380032260897357574,
   0.013552581146419991759,
   0.01372704726634531476,
   0.013903447513498605817,
   0.014081798870737662066,
   0.014262118410668883292,
   0.014444423295351498104,
   0.014628730775989261942,
   0.014815058192609928747,
   0.015003422973732204876,
   0.015193842636020263304,
   0.015386334783925457309,
   0.015580917109315466085,
   0.015777607391090516659,
   0.015976423494786635288,
   0.016177383372166093123,
   0.016380505060794546546,
   0.01658580668360502483,
   0.016793306448448817175,
   0.017003022647632797665,
   0.017214973657443403271,
   0.017429177937657098357,
   0.017645654031037068948,
   0.017864420562816559629,
   0.018085496240168086324,
   0.018308899851658979457,
   0.01853465026669295912,
   0.018762766434937759585,
   0.018993267385738542979,
   0.019226172227517296376,
   0.019461500147157879265,
   0.019699270409376908736,
   0.019939502356080107681,
   0.020182215405704410915,
   0.020427429052545346966,
   0.020675162866070049411,
   0.02092543649021553695,
   0.021178269642672251788,
   0.021433682114152998593,
   0.021691693767646784419,
   0.021952324537658211845,
   0.022215594429431499007,
   0.022481523518159737124,
   0.022750131948179215524,
   0.023021439932148356211,
   0.023295467750211833885,
   0.023572235749149201417,
   0.023851764341508534251,
   0.024134074004724767604,
   0.024419185280222559936,
   0.024707118772503911669,
   0.024997895148220431599,
   0.025291535135230129583,
   0.025588059521638624461,
   0.025887489154825162746,
   0.026189844940452695204,
   0.026495147841462854399,
   0.026803418877054951963,
   0.027114679121649644389,
   0.027428949703836830176,
   0.02774625180530789284,
   0.028066606659772497939,
   0.028390035551859420238,
   0.028716559816001813871,
   0.029046200835306811017,
   0.029378980040409417851,
   0.029714918908310634926,
   0.030054038961199812385,
   0.030396361765261392662,
   0.030741908929465964345,
   0.031090702104345478013,
   0.031442762980752707314,
   0.031798113288605288351,
   0.032156774795613692064,
   0.032518769305993865115,
   0.032884118659163893983,
   0.033252844728425247356,
   0.033624969419628329692,
   0.034000514669822436142,
   0.034379502445890025575,
   0.034761954743165519865,
   0.035147893584038795989,
   0.035537341016542760286,
   0.035930319112925809821,
   0.036326849968208736741,
   0.036726955698726304611,
   0.03713065844065358001,
   0.037537980348516804263,
   0.037948943593689124509,
   0.038363570362871239616,
   0.038781882856556773587,
   0.039203903287482654016,
   0.039629653879064530297,
   0.040059156863817078909,
   0.040492434481759757847,
   0.040929508978807364883,
   0.041370402605146114339,
   0.041815137613594961785,
   0.042263736257952440323,
   0.042716220791328952944,
   0.043172613464464396071,
   0.043632936524031926129,
   0.04409721221092709198,
   0.044565462758543061828,
   0.045037710391031507418,
   0.045513977321549825561,
   0.04599428575049440554,
   0.046478657863720060361,
   0.046967115830745816141,
   0.047459681802947323304,
   0.047956377911735646735,
   0.048457226266722816521,
   0.048962248953874264179,
   0.049471468033648102747,
   0.049984905539121354812,
   0.05050258347410369747,
   0.051024523811238148285,
   0.051550748490089379206,
   0.052081279415219554341,
   0.052616138454252045498,
   0.053155347435922810362,
   0.053698928148119738635,
   0.054246902335910396342,
   0.054799291699558001778,
   0.055356117892525667779,
   0.055917402519469486255,
   0.056483167134220232941,
   0.057053433237754240526,
   0.057628222276153169557,
   0.058207555638553037936,
   0.058791454655082897585,
   0.059379940594793054198,
   0.059973034663572864778,
   0.060570758002058994185,
   0.06117313168353344377,
   0.061780176711811893298,
   0.062391914019123084767,
   0.06300836446397840851,
   0.063629548829032656077,
   0.064255487818935849709,
   0.064886202058176509211,
   0.065521712088916508887,
   0.066162038368817191469,
   0.066807201268858085186,
   0.067457221071147488445,
   0.068112117966725463369,
   0.068771912053359196548,
   0.06943662333333175396,
   0.07010627171122316148,
   0.070780876991685559574,
   0.071460458877211016637,
   0.072145036965893777348,
   0.07283463074918612723,
   0.073529259609648345286,
   0.07422894281869360511,
   0.074933699534327061209,
   0.075643548798879897688,
   0.076358509536739116452,
   0.077078600552071885321,
   0.077803840526546430567,
   0.078534248017048099988,
   0.079269841453392442254,
   0.080010639136033664953,
   0.080756659233771094231,
   0.081507919781451387831,
   0.082264438677668930144,
   0.083026233682463285168,
   0.083793322415014290239,
   0.084565722351335720353,
   0.085343450821966995723,
   0.086126525009663307264,
   0.086914961947085034311,
   0.087708778514486190891,
   0.088507991437402053214,
   0.089312617284337147971,
   0.09012267246445247737,
   0.090938173225253993159,
   0.09175913565028083474,
   0.092585575656794941168,
   0.093417508993471787271,
   0.094254951238092840593,
   0.095097917795239059191,
   0.095946423893987706211,
   0.096800484585610330202,
   0.0976601147412745757,
   0.09852532904974783956,
   0.099396142015105604095,
   0.10027256795444211557,
   0.10115462099558590603,
   0.10204231507481917318,
   0.10293566393460183706,
   0.10383468112130042615,
   0.10473937998292234819,
   0.10564977366685526783,
   0.10656587511761302089,
   0.10748769707458694089,
   0.1084152520698039579,
   0.10934855242569195555,
   0.11028761025285126196,
   0.11123243744783462006,
   0.11218304569093426326,
   0.11313944644397733175,
   0.11410165094812961539,
   0.11506967022170831727,
   0.11604351505800336586,
   0.11702319602310878865,
   0.1180087234537631341,
   0.11900010745520073208,
   0.11999735789901246064,
   0.1210004844210181979,
   0.12200949641914927979,
   0.12302440305134344778,
   0.12404521323345034378,
   0.12507193563715032769,
   0.12610457868788446656,
   0.12714315056279831828,
   0.1281876591886974559,
   0.12923811224001785503,
   0.13029451713680884062,
   0.13135688104273071652,
   0.132425210863066245,
   0.13349951324274719755,
   0.13457979456439614352,
   0.13566606094638267166,
   0.13675831824089645927,
   0.13785657203203549592,
   0.13896082763391104375,
   0.14007109008876905687,
   0.14118736416512900345,
   0.14230965435593920243,
   0.14343796487675103402,
   0.14457229966390955367,
   0.14571266237276417344,
   0.14685905637589588557,
   0.14801148476136605225,
   0.14916995033098143231,
   0.15033445559858149565,
   0.15150500278834366785,
   0.15268159383311036281,
   0.15386423037273486147,
   0.15505291375244961705,
   0.15624764502125459975,
   0.15744842493032787378,
   0.15865525393145704647,
   0.15986813217549400434,
   0.16108705951083091001,
   0.16231203548189923613,
   0.16354305932769230836,
   0.16478012998031038583,
   0.1660232460635296392,
   0.16727240589139508176,
   0.1685276074668378421,
   0.16978884848031608468,
   0.17105612630848185396,
   0.17232943801287187169,
   0.17360878033862461867,
   0.17489414971322200798,
   0.17618554224525792562,
   0.17748295372323227848,
   0.17878637961437177095,
   0.18009581506347693836,
   0.18141125489179726893,
   0.18273269359593191652,
   0.18406012534675952885,
   0.18539354398839455462,
   0.18673294303717269393,
   0.18807831568066338268,
   0.18942965477671219743,
   0.1907869528525106273,
   0.19215020210369621045,
   0.1935193943934806482,
   0.19489452125180836695,
   0.1962755738745444456,
   0.19766254312269240789,
   0.19905541952164243491,
   0.20045419326044963682,
   0.20185885419114377171,
   0.20326939182806844086,
   0.20468579534725270253,
   0.206108053585813078,
   0.20753615504138780978,
   0.20897008787160162302,
   0.21040983989356371042,
   0.21185539858339666464,
   0.21330675107579877281,
   0.21476388416363711986,
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